.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/electrochem/electrolysis/plot_02_water_electrolysis.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_api_gallery_electrochem_electrolysis_plot_02_water_electrolysis.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_api_gallery_electrochem_electrolysis_plot_02_water_electrolysis.py:


Nicholson and Carlisle's electrolysis of water
==================================================

Days after learning of Volta's newly announced pile, William Nicholson
and Anthony Carlisle connected one to a bowl of water in May 1800 and
watched gas bubble from each wire -- the first electrolysis, and the
first new discovery the pile made possible. This example reconstructs
both halves of that observation from functions already in this package:
the theoretical minimum decomposition voltage of water
(:func:`~chemistrykit.electrochem.systems.electrolysis.minimum_applied_voltage_electrolytic`,
applied to the tabulated H+/H2 and O2/H2O standard potentials) comes out
at the textbook 1.23 V, and Faraday's law
(:func:`~chemistrykit.electrochem.systems.electrolysis.moles_from_charge`)
recovers the 2:1 hydrogen-to-oxygen ratio Nicholson and Carlisle actually
saw bubbling from the two wires, directly from electron-transfer
stoichiometry.

.. GENERATED FROM PYTHON SOURCE LINES 21-35

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from chemistrykit.electrochem.systems.electrolysis import (
        charge_from_current,
        minimum_applied_voltage_electrolytic,
        moles_from_charge,
    )
    from chemistrykit.electrochem.systems.standard_potentials import (
        STANDARD_REDUCTION_POTENTIALS,
        cell_potential,
        is_spontaneous,
    )








.. GENERATED FROM PYTHON SOURCE LINES 36-41

The overall water-splitting reaction, 2 H2O -> 2 H2 + O2, splits into a
cathodic reduction (2 H+ + 2 e- -> H2) and an anodic oxidation
(2 H2O -> O2 + 4 H+ + 4 e-, the reverse of the tabulated O2/H2O
reduction) -- both half-reactions are already in this package's
standard-potential table.

.. GENERATED FROM PYTHON SOURCE LINES 41-50

.. code-block:: Python

    h2 = STANDARD_REDUCTION_POTENTIALS["H+/H2"]
    o2 = STANDARD_REDUCTION_POTENTIALS["O2/H2O"]
    E_water = cell_potential(cathode=h2, anode=o2)
    V_min = minimum_applied_voltage_electrolytic(E_water)
    print(f"Water-splitting cell potential (cathode H+/H2, anode O2/H2O): {E_water:.2f} V")
    print(f"Spontaneous as written: {is_spontaneous(E_water)}")
    print(f"Minimum applied voltage to force electrolysis: {V_min:.2f} V")
    print("(the accepted standard decomposition voltage of water is 1.23 V)")





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    Water-splitting cell potential (cathode H+/H2, anode O2/H2O): -1.23 V
    Spontaneous as written: False
    Minimum applied voltage to force electrolysis: 1.23 V
    (the accepted standard decomposition voltage of water is 1.23 V)




.. GENERATED FROM PYTHON SOURCE LINES 51-56

Faraday's law applied to the two evolved gases: the same charge passed
produces H2 (n=2 electrons per molecule) at twice the molar rate of O2
(n=4 electrons per molecule) -- exactly the 2:1 volume ratio Nicholson
and Carlisle observed bubbling from the two wires (equal moles of gas
occupy equal volume, by Avogadro's law).

.. GENERATED FROM PYTHON SOURCE LINES 56-65

.. code-block:: Python

    current, time_s = 0.5, 600.0  # A, s
    Q = charge_from_current(current, time_s)
    moles_H2 = moles_from_charge(Q, n=2)
    moles_O2 = moles_from_charge(Q, n=4)
    print(f"\nCharge passed in {time_s:.0f} s at {current} A: {Q:.1f} C")
    print(f"Moles H2 evolved: {moles_H2:.3e} mol")
    print(f"Moles O2 evolved: {moles_O2:.3e} mol")
    print(f"H2:O2 mole (and volume) ratio: {moles_H2 / moles_O2:.2f}")





.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    Charge passed in 600 s at 0.5 A: 300.0 C
    Moles H2 evolved: 1.555e-03 mol
    Moles O2 evolved: 7.773e-04 mol
    H2:O2 mole (and volume) ratio: 2.00




.. GENERATED FROM PYTHON SOURCE LINES 66-77

.. code-block:: Python

    fig, ax = plt.subplots()
    times = np.linspace(0.0, time_s, 100)
    Q_t = charge_from_current(current, times)
    ax.plot(times, moles_from_charge(Q_t, n=2) * 1e3, label="H2")
    ax.plot(times, moles_from_charge(Q_t, n=4) * 1e3, label="O2")
    ax.set_xlabel("Time (s)")
    ax.set_ylabel("Gas evolved (mmol)")
    ax.set_title("Faraday's law: gas evolution during water electrolysis")
    ax.legend()
    fig.tight_layout()
    plt.show()



.. image-sg:: /api/gallery/electrochem/electrolysis/images/sphx_glr_plot_02_water_electrolysis_001.png
   :alt: Faraday's law: gas evolution during water electrolysis
   :srcset: /api/gallery/electrochem/electrolysis/images/sphx_glr_plot_02_water_electrolysis_001.png
   :class: sphx-glr-single-img






.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.038 seconds)


.. _sphx_glr_download_api_gallery_electrochem_electrolysis_plot_02_water_electrolysis.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_02_water_electrolysis.ipynb <plot_02_water_electrolysis.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_02_water_electrolysis.py <plot_02_water_electrolysis.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_02_water_electrolysis.zip <plot_02_water_electrolysis.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_